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A278188 T(n,k)=Number of nXk 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%I A278188 #4 Nov 14 2016 22:31:54
%S A278188 0,0,0,0,3,0,0,19,28,0,0,136,544,200,0,0,935,13012,13720,1532,0,0,
%T A278188 6381,295190,1075258,347116,11794,0,0,43478,6715738,81691958,91270219,
%U A278188 8803344,90538,0,0,296105,152540636,6196345742,23124026160,7737459027,223230876
%N A278188 T(n,k)=Number of nXk 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
%C A278188 Table starts
%C A278188 .0.......0............0................0..................0...................0
%C A278188 .0.......3...........19..............136................935................6381
%C A278188 .0......28..........544............13012.............295190.............6715738
%C A278188 .0.....200........13720..........1075258...........81691958..........6196345742
%C A278188 .0....1532.......347116.........91270219........23124026160.......5858713218010
%C A278188 .0...11794......8803344.......7737459027......6545874548694....5537142857552112
%C A278188 .0...90538....223230876.....656008970388...1852662745588838.5232919178331757631
%C A278188 .0..695252...5660949042...55620335387114.524386828923495662
%C A278188 .0.5339294.143557203008.4715820197535009
%H A278188 R. H. Hardin, <a href="/A278188/b278188.txt">Table of n, a(n) for n = 1..84</a>
%F A278188 Empirical for column k:
%F A278188 k=2: a(n) = 8*a(n-1) -4*a(n-2) +15*a(n-3) -26*a(n-4) +14*a(n-5) -16*a(n-6)
%F A278188 k=3: [order 27]
%F A278188 Empirical for row n:
%F A278188 n=2: a(n) = 9*a(n-1) -16*a(n-2) +9*a(n-3) -12*a(n-4) +5*a(n-5) +7*a(n-6) -4*a(n-7)
%F A278188 n=3: [order 43]
%e A278188 Some solutions for n=3 k=4
%e A278188 ..0..3..3..0. .0..1..3..2. .0..1..0..3. .0..1..0..3. .0..3..1..0
%e A278188 ..1..3..2..1. .1..2..0..3. .3..2..0..3. .3..2..2..1. .1..2..2..0
%e A278188 ..2..2..0..1. .3..0..1..3. .1..2..2..3. .1..1..1..1. .1..2..3..3
%K A278188 nonn,tabl
%O A278188 1,5
%A A278188 _R. H. Hardin_, Nov 14 2016